One known example of a filter for a base station in mobile communications is a filter that includes a dielectric resonator in which electromagnetic fields of a plurality of TE01δ modes exist so as to be focused within the dielectric core (dual-mode TE01δ resonator). The dual-mode TE01δ resonator used in this filter achieves a characteristic of high unloaded Q (hereinafter referred to simply as “Qu”) by use of a dielectric material having a small dielectric loss tangent (tan δ), so the filter can have a lower loss and excellent frequency selectivity. The representation TE01δ mode used here indicates one in a cylindrical (i.e., designated by axes θ, r, z) coordinate system (represented as TEθrz), and the same resonant mode is the TE110 mode when being represented in a Cartesian (i.e., designated by axes x, y, z) coordinate system (represented as TExyz).
Configurations in which a groove is provided in a part of a dielectric resonator and two resonant modes are coupled are disclosed in Patent Document 1 and Patent Document 2.
The configuration of the dielectric resonator illustrated in Patent Document 1 is described here on the basis of the perspective view of FIG. 1. A dielectric resonator 51 has the shape of a column of cruciform cross section, and two flat plate portions 52A and 52B form a dual-mode TE01δ resonator. The flat plate portions 52A and 52B have grooved portions 56A and 56B at their inner corners. The dielectric resonator 51 is bonded on a support table 55.
With such a configuration, a first TE01δ mode in which an electric-field vector rotates within the flat plate portion 52A occurs, and a second TE01δ mode in which an electric-field vector rotates within the flat plate portion 52B occurs. The electric-field vectors in the two TE01δ modes are distorted by the grooved portions 56A and 56B, and the above two TE01δ modes are coupled. The amount of this coupling is set by the depth and width dimensions of the grooved portions 56A and 56B.
Patent Document 2 discloses a dielectric resonator in which two TM110 modes are coupled by grooved portions.
Patent Document 1: Japanese Unexamined Patent Application Publication No. 2004-186712
Patent Document 2: Japanese Unexamined Patent Application Publication No. 7-202530
In general, for a band-pass filter that includes a plurality of stages of dielectric resonators, the amount of coupling between the resonators and the relative bandwidth of the filter are proportional to each other. Therefore, to obtain a filter having a large relative bandwidth, a dielectric resonator having a large amount of coupling is necessary. For example, to obtain a filter having a pass band of 60 MHz at 2 GHz range (the relative bandwidth is 3%), it is necessary to strongly couple the resonators with approximately 3%.
The effects of setting the amount of coupling by adjusting the depth dimension of the grooved portions in the configuration illustrated in Patent Document 1 is described here with reference to FIGS. 2(A) and 2(B). FIG. 2(A) is a front view of the dielectric resonator 51 illustrated in FIG. 1. When the dimension of an original diagonal line between the inner corners having no grooved portions in each of the flat plate portions 52A and 52B is Lh and the grooved portions 56A and 56B have the same depth dimension Lp, the ratio of the depth dimension of each of the grooved portions to the dimension of the original diagonal line (depth ratio Dp) is represented by the following expression:Dp=2Lp/Lh 
Here, the relationship between the depth ratio Dp and the amount of coupling is illustrated in FIG. 2(B). The horizontal axis indicates the depth ratio Dp, and the vertical axis indicates the amount of coupling.
When the depth ratio Dp is 0%, i.e., the grooved portions 56A and 56B are not formed, the amount of coupling is zero, and no coupling occurs. When the depth ratio Dp is below approximately 50%, the amount of coupling is at or below 0.5%, so only a small amount of coupling is set. To set the amount of coupling larger than 0.5%, it is necessary to set the depth ratio Dp at or above 50%.
In the case of the dielectric resonator illustrated in Patent Document 1, the amount of coupling can be set by adjusting the depth dimension of the grooved portion, as described above. However, to achieve the dielectric resonator having a large amount of coupling, it is necessary to set the depth dimension of the grooved portion at a significantly large value. For example, to obtain a filter characteristic of a relative bandwidth of 3%, it is necessary to achieve a dielectric resonator having an amount of coupling of approximately 3% by setting the depth ratio Dp of the grooved portion at approximately 75%, i.e., setting the material thickness between the inner corners of each of the flat plate portions at approximately ¼ of the dimension of the original diagonal line.
In production of the dual-mode TE01δ resonator having such a significantly deep grooved portion, a crack is apt to appear in the grooved portion and a cracking defect often occurs in the dielectric resonator during sintering of the dielectric resonator or during turning of the depth dimension (cutting) of the grooved portion. Therefore, the production is difficult.
In detail design of the dielectric resonator illustrated in Patent Document 1, it is necessary to repeat the following redesign loop.
1. Deepen the grooved portion.→2. The resonant frequency increases.→3. Increase the material thickness to lower the resonant frequency.→4. The amount of coupling reduces.→5. Deepen the grooved portion.
This process causes the dielectric resonator to have a significantly large material thickness, so the size of the dielectric resonator is larger, compared with that of a standard-shaped dielectric resonator having the same resonant frequency and having no grooved portion. Therefore, the dielectric resonator illustrated in Patent Document 1 may fail to form a smaller filter.
To accommodate the dielectric resonator having a large size in a cavity, unless the size of the cavity is large, the proportion of the dielectric resonator in the cavity is increased. This reduces the frequency in the spurious mode (TM mode) occurring in the cavity, and adverse effects are exerted on a required attenuation range.
For the dielectric resonator having an overall material thickness larger than that of a standard-shaped one, the Qu characteristic is poorer than that of the standard-shaped dielectric resonator. As a result, there is a limit to a reduction in loss of a filter using the dielectric resonator illustrated in Patent Document 1.